public IMatrix Solve(IMatrix b)
{
if (b.Rows != _lu.Rows) throw new ArgumentException("Invalid matrix dimensions.");
if (!IsNonSingular) throw new InvalidOperationException("Matrix is singular");
// Copy right hand side with pivoting
int count = b.Columns;
IMatrix x = b.Submatrix(_pivotVector, 0, count - 1);
//int rows = LU.Rows;
int columns = _lu.Columns;
double[][] lu = _lu.Array;
// Solve L*Y = B(piv,:)
for (int k = 0; k < columns; k++)
{
for (int i = k + 1; i < columns; i++)
{
for (int j = 0; j < count; j++)
{
x[i, j] -= x[k, j]*lu[i][k];
}
}
}
// Solve U*X = Y;
for (int k = columns - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
x[k, j] /= lu[k][k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
x[i, j] -= x[k, j]*lu[i][k];
}
}
}
return x;
}
